Piezoelectric crystal apparatus



Dec. 30, 1941. w. P. MASON PIEZOELECTRIC CRYSTAL APPARATUS 2 sheets-'sheet 1 Filed March 29, 1940 \N, m E R P M O C Y B m u u ...1. u.. n 4 Si mE Lao?. ko m55. Q

/NVENTOR By WPMA SON w @ALL/il A TTRNE V Dec. 30, 1941. w. P. MASON 2,268,413

PIEZOELEGTRIG CRYSTAL APPARATUS Filed March 29, 1940 2 sheets-sheet 2 FIG. 6

/NVE/vrof? W l? MA SON v w. QQM

ATTORNE V Patented Dec. 0, 1941 UNITED STATES' PATENT OFFICE PIEZOELECTRIC CRYSTAL APPARATUS Warren P. Mason, West Orange, N. J., assignor to Beil Telephone Laboratories, Incorporated, New .1York, N. Y., a corporation of New York Application March 29, 1940, Serial No. 326,764

16 Claims.

This invention relates to piezoelectric crystal apparatus and particularly to vibratory piezoelectric quartz crystal elements suitable for use as circuit elements in such systems as electric wave filter systems and oscillation Vgenerator systems, for example.

One ofthe objects of this invention is to provide piezoelectric crystals having a low or substantially zero temperature coefficient of frequency.

Another object of this invention is to provide relatively low frequency piezoelectric crystals having a very constant vibrational frequency throughout a'wide range of temperatures.

Another object of this invention is to provide piezoelectric crystals substantially free from in` terfering vibrational modes or free from any harmful or undesiredrfrequencles near to the des ired frequency.

Another object of this invention is to provide l piezoelectric crystal elements of relatively small \convenient ratios from the desired main mode of vibration where they will cause no harm. It

i is also desirable that such crystal elements,

when utilized at the relatively lower frequencies such as, for example, below about 100 kilocycles per second, be of relatively small and convenient size in order to avoid the expense that is usually involved in crystal elements of the relatively larger sizes. Y

The piezoelectric crystal elements provided in 4. accordance with thls invention may have a' 10W orientation of piezoelectric quartz crystal"L eletemperature coefficient of frequency over a wide range of dimensional ratios, and on account of this feature, they are advantageous for use in filter systems since any undesired secondary resonance frequency therein may, by adjustment ofthe dimensional ratio, be placedat a remoteA position where it will cause no harm, without disturbing the temperature coefficient of the desired resonant frequency. Also since the crystal elements provided in accordance with this invention may have a relatively small size at low frequencies, they may be constructed economically down to 50 kiloeycles per second or less, and accordingly are advantageous for use in low fre- .i quency oscillators, filtersy and other low frequency systems.

In accordance with this invention, relatively y thin piezoelectric quartz crystal plates of suitable `orientation with respect to the X, Y and Z axes IU of the quartz material and of suitable dimensional ratios may be subjected to a thickness direction electric field and vibrated at a resonance frequency dependent mainly upon the longest or major axis length dimension of the crystal l5 plate in a mode of motion which is herein called a longitudinal mode. The orientation angles and the dimensional ratios of the crystal plate may be any of severalto produce for the longitudinal mode of motion a low or substantially 2" zero temperature coefficient of frequency at temperatures within a range between about 0 and +80 degrees: centigrade over a wide ratio of the width to length dimensions of its major faces, the frequency of the fundamental mode vibration if" along the length or longest Vdimension of the crystal element being approximately or roughly 275 .kilocycles per second per centimeter of the length or longest dimension. In a particular embodiment, the ratio of the width dimension W 3" with respect to length dimension L of the major surfaces may range from about 0.35 to ,0.57 and the orientation may be that of an X cut crystal element rotated in effect about +8.5 degrees about its X axis or thickness dimension and 37 then rotated from about 32 to 40 degrees about j the major axis Y' or length dimension L.

For a clearer understanding of the nature of this invention and the additional advantages, features and objects thereof, reference is made m to the following description taken in connection with the accompanying drawings, in which/like .reference characters represent like or similar parts and in which: Fig. 1 is a perspective view showing the ments cut in accordance with this invention;

Fig. 2 is a graph illustrating some preferred orientation angles and dimensional ratios of .no crystal elements in accordance with this inven- 55 F185. 4 and 5 are front and side elevation views of a holder which may be used for mounting thejcrystal element; and

Fig. (iy is a schematic diagram of the electrical connections of the crystal unit shown in Figs. 4 and 5.

This specification follows the conventional terminology as applied to crystalline quartz which employs three orthogonal or mutually perpendicular X, Y and Z axes, as shownv in the I drawings, to designate an electric, a mechanical i and the optic axes, respectively, of piezoelectric quartz crystal material, and which employs three orthogonal axes X', Y' and Z' to designate the directions of axes of a piezoelectric body angularly oriented with respect to such X, Y and Z axes thereof. Where the orientation is obtained by double rotations of the quartz crystal element I, one rotation being ineifect substantially about an electric axis X, and the other about another 'to the z axis, as illustrated in Fig. 1. is toward parallelism with the plane of a minor apex face of the natural quartz crystal, and a negative 0 angle rotation of the Z' axis with respect 5 to the Z axis is toward parallelism with the plane of a major apex face of the natural quartz crystal.

Referring to the drawings,` Fig. 1 is a perspective view showing a thin piezoelectric quartz crystal element I cut from crystal quartzfree of twinning, veils or other inclusions and made into a substantially rectangular parallelepiped shape having a length or longest dimension L,

Y a width dimension W which is perpendicular to the length dimension L, and a thickness or thin Adimension T which is perpendicular' to the other two dimensions L and W.

The final length dimension L of the crystal element i is v4determined by and is made of a value according to the desired resonant frequency. The width dimension W is preferably related to the length dimension L in accordance with the values of dimensional ratios as given herein. The thickness dimension T may be of the order of 1 millimeter or other suitable value to suit the impedance of the circuit in which the crystal element I is utilized.

'I'he length dimension Lfof the crystal element I lies along a Y axis in the plane of a mechaniical axis Y and the optic axis Z of the quartz of polarization of a plane polarized light ray traveling along the optic axis Z inthe crystal is rotated in a right-hand direction, or clockwise as viewed by an observer located at the light source and facing the crystal. This definition ofrighthanded quartz follows the convention which originated with Herschel. Trans. Cam. Phil. Soc. vol. 1, page 43 (1821); Nature vol. 110, page 807 (1922); Quartz Resonatorsland Oscillators, P. Vigoureux, page 12 (1931). a quartz crystal is designated as left-handed if it rotates such plane of polarization referred to in the left-handed or counter-clockwise direction,' namely, in the direction opposite to that given hereinbefore for the right-handed crystal. 45

If a compressional stress or a squeeze be applied to the ends of an electric axis X of a. quartz body I and not removed, a charge will be de veloped which is positive at the positive end of the X axis and negative at the negative end of such electric axis X, for either righthanded or left-handed crystals. The magnitude and sign of the charge may be measured in a known manner with a vacuum tube electrometer,

for example. In specifying'the orientation of a 55 right-handed crystal, the sense of the angle 0 which the new axis Z' makes with respect to the optic axis Z as the crystal plate is rotated in el'- vfect about the X axis is deemed positive when, with the compression positive end of the X axis pointed toward the observer, the rotation is in a clockwise direction, as illustrated in Fig. 1. vA counter-clockwise rotation of such a right-handed crystal about the X axis gives rise to a negative orientation angle 0 with respect o5 to the Y axis or the Z axis. Conversely, the orientation angle of a left-handed crystal is positive when, with the compression positive end of the electric axisA X pointed toward the observer, the rotation is counter-clockwise, and is negative when the rotation is clockwise. The crystal material illustrated in Fig. 1 is righthanded as the term is used herein. For either right-handed or left-handed quartz, a positive angle 0 rotation of the Z' axis with respect 75 Conversely, 40

crystal material from which the element I is cut and is inclined at an angle of +0 degrees with respect to said Y axis, the angle 0 being one oi' the values between substantially 0 and +10 degrees.

The major surfaces and the major plane of the crystal element I are disposed or inclined at an angle fp with respect to the plane of the Y'and Z axes mentioned, the angle p being the angle between the width dimension W lying along the Z" axis andthe Z axis which lies in kthe' plane of the Y and Z axes mentioned, the Z' axis being inclined at the angle 0 with respect to the optic axis Z. The axis Z" is accordingly the result of a double rotation of the width dimension W irst about the X axis +0 degrees, and then o degrees about the length dimension L or Y' axis.` It will be noted that the crystal element I isin e'ect an X cut crystalvrotated +0 de- Brees about the X axis and then rotated p degrees about the Y' axis length dimension L.

The crystal plate i is shown in Fig. 1 as being inclined at a p angle on opposite sides of the Z axis. It will be understood that either of these positions for the p angle may be used alternatively with any c angle disclosed herein.

' Suitable/conductive electrodes, such as the electrodes 3 and it of Fig. 1 or the electrodes 20, 2i, 22 and 23 of Figs. 4 to 6. for example, maybe placed on or adjacent to or formed integral with the opposite major surfaces of the crystal' plate I in order to apply electric field excitation to the quartz plate I in the direction of the` thickness dimension T, and by means of any suitable circuit such as, for example, a lter or an oscillator circuit, the quartz plate l may be vibrated in the desired fundamental longitudinal mode of motion at a resonant response frequency which depends mainly upon and varies inversely as the major axis length dimension L, the frequency being a value within a range roughly from about 250 to 280 kilocycles per second per centimeter of the length dimension L, the particular value depending upon the orientation angles 0 and c of the crystal element I.

moans The crystal electrodes tand 4 when formed integral with the maior surfaces of the crystal element I may consist of thin coatings of silver. aluminum or other suitable metal deposited upon the bare quartz by'evaporation in vacuumor by other suitable'process, and may wholly or partially cover the maior surfaces of the crystal element I. Examples of partial electrodes for driving the crystal element I in the fundamental or harmonic longitudinal mode of motion along theslength dimension L are illustrated in application sensi No.'219,325 nlgi/iuiy 15. 193s, by R. A. Sykes now United States Patent No. 2,223,537. dated December 3, 1950. l

' The crystal electrodes 3 and I may be longitudinally centrally divided or split along the length dimension L to )form four separate lelectrodes in order to obtain two separate circuits of equal frequency from thesingle crystal element I or for other purposes.` Figs. 4 to 6 illustrate such a division-of the electrodes but with the two larger electrodes overlapping and interconnected to reduce the capacity of the electrode crystal element I. The bare crystal element I Amay be etched in a solution of commercial hydrofluoric acid for a period of approximately 20 minutes before applying the electrode coatings thereto. I

'I'he crystal element I may be supported by any suitable means such as, for example, by clamping or otherwise supporting it along the nodal line which is located centrally midway between the small ends of the crystal element I o! width W to length L about 0.5, the temperature coemcient of the longitudinal mode becomes more highly negative.

When the longitudinally vibrated crystal ele ment I of Fig. 1 has a 6 angle between about 0 and degrees, and e. o angle between about 30 and 50 degrees, the crystals may have a low or substantially zero temperature coetllcient of frequency over a wide range of dimensional ratios of the Width W with respect to the length L thereof as illustrated by the curves A, B, C and D of Fig. 2.

Fig. 2 is a graph showing the relation between some of the 6 and p angles of cut and the corresponding values of the dimensional ratios ot' `the width W with respect to the length L that may be utilized in connection with the crystal element I of Fig. 1 in order to obtain a substantially zero temperature coemcient of frequency for the longitudinal mode vibration thereof, the

fundamental mode frequency being a value within the range between about 250,and 280 kllocycles per centimeter of the length dimension L. In Fig. 2, it will be noted that the e angles illustrated range from about 32 to 47 degrees for 6 angles from 0 to +8.5 degrees with dimensional ratios within a range from about 0.25 to 0.85 according to the 6 and q angles selected.

For example, whenl the 6 angle is substantially +85 degrees as shown in the curve A of Fig. 2,

. the ratio of the width dimension W with respect and inclined about 11 degrees more or less with When the relatively thin longitudinally'vibrated quartz crystal element I has a p angle of substantially zero degrees and any 6 angle between about 0 and +10 degrees, and the dimensional ratio'of the width dimension W with' respect 45 to the length dimension' L is relatively small as, for example, about 0.15. the temperature coeillcient of the longitudinal inode vibrational frequency along the length dimension L is low or less than 0.7 part-per million per degree centigrade 'at a temperature of about 30 degrees centigrade for all of such angles of c up to about +10 degrees and where such angle of 6 is sub stantiallyr or very slightly greater than +8 degrees, the temperaturecoeilicient of such longitudinal mode vibrational l:frequency is only about 0.2 part per million per degree centigrade over a wide range of ordinary temperatures. Such crystals and particularly the one having the 6 angle of substantially +8.5 degrees, the o angle being roughly zero degrees, are useful as oscillators or in other circuit element applications where a very low temperature coemcient of fre-NV l quency is desired`with a relatively high irnpedance in a long, thin and very narrow width form of crystal element. y

If the width dimension W relative to the length dimension L of such crystal elements having a p angle of substantially zero degrees and a 6 angle within the range from about `0 to +10 degrees, be increased to values between 0.3 and K0.5, the temperature coeillcient of the length or longitudinal mode frequency becomes of the order of about -4 up' to -10 parts per million per degree centigrade at a temperature of about 30 to the length dimension L of the crystal element I may be between 0.33 and 0.52 for a p angle from 32 to 36 degrees.

When the 6 angle is substantially +7.5 degrees as shown in the curve B of Fig. 2, the ratio of the width dimension W with respect to the length dimension L of the crystal element I may be within a range from about 0.32 to 0.56 for a c angle from 35 to 40 degrees.

. Similarly, as shown by the curve C of Fig. 3 when the 6 angle is substantially +5 degrees, the ratio of the width dimension W with respect to the length dimension L of the crystal elemerit I may be within the range from about 0.33

to 0.60 for p angles between about 39.5 degrees and 45 degrees.

When the 6 angle is substantially 0 degrees as shown in the curve D of Fig. 2, the ratio of the width dimension W with respect tothe length dimension L of the crystal element I may .be

within a range from about 0.25 to 0.85 for a.

p angle from 45 to 47.5 degrees.

It will be noted that the curves A, B, C and length L dimensional ratios corresponding to certain 6 and p angles for which the crystal element will have substantially zero temperature coefficient of frequency for longitudinal mode vibrations.

While the curves A, B, C. and D of Fig. 2 illustratey the corresponding values of p angles and dimensional ratios of width W to length L that width Wwith respect to the` length L of the crystal element may be any value near to or between 0.33 and 0.52.

It will be noted from the curves of Fig. 2 that for any angle between about 0 and +10 degrees the dimensional ratio of the width W with respect to the length L may be between about 0.35 and 0.50 with a wide range of suitable c angles as indicated by the ordinate values given in Fig. 2. It will be understood that the longitudinal mode resonant frequency hereinbefore referred to of all of Such crystals will have a low temperature coefficient at one or more temperatures within a wide range of' temperatures between roughly 0 and 80 centigrade.

Fig. y3 is a graph showing the characteristics of a quartz crystal element I having a dangle of substantially +8.5 degrees and a p angle of substantially 36 degrees and having various values for the ratio of its Width dimension W with respect to its length dimension L, as given by the curve A of Fig. 2. The curve labeled Fyy of Fig. 3 shows the relation between the desired fundamental longitudinal mode resonant frequency Fyy thereof, expressed in kilocycles per second per centimeter of the length dimension L, and the ratio of the Width dimension W` with respect to the length dimension L. For example, when the dimensional ratio of the Width W to the length L is about 0.38, the longitudinal mode resonant frequency Fyy of a crysta1 ele-f ment I having a length dimension L of one centimeter and having 0 and o angles of substantially +8.5 and 36 degrees respectively, is about 282 kilocycles per second. Since the frequency is inversely proportional to the length dimension L, a crystal element of the same orientation and dimensional ratio but having a length dimension L of four centimeters for example will have a longitudinal mode resonant frequency .F1/y of one-fourth this value or about 70.5 kilocycles per second. Similarly, the frequency and the corresponding length dimension L may be obtained for any other size of crystal element.

The curve Tyy of Fig. 3 shows the relation between the temperature coefficient of th longitudinal mode resonant frequency Fyy and the ratio of the width dimension W with respect to the length dimension L. It will be noted that for all of the dimensional ratios of W to L between about 0.33 and 0.52, as shown by the curve labeled Tyy of Fig. 3 and somewhat beyond these values as is shown by the curve Tyy of Fig. 3, the crysta1 element I having a 0 angle of substantially +8.5 degrees and a go angle of substantially 36 degrees has a low or substantially zero temperature coeiiicient over a wide range of ordinary temperatures above and below 30 centigrade. As shown by the curve Tyy of Fig. 3, this crystal element has a maximum positive temperature coeicient of frequency of about +0.6 part per million per degree centigrade within the range of dimensional ratios between about 0.34 and 0.52, the zero temperature coeiicient of frequency occurring at the dimensional ratio values of about 0.34 and 0.52.

As shown in Fig. 3, in addition to the resonant frequency labeled Fyy, there is also another prominent resonant frequency labeled Fyz, the

former being the longitudinal mode vibration along the length dimension L of the crystal element I and the latter being the face shear mode whichv may be coupled to a flexural mode for of frequency Tyy respectively of Fig. 3. When the dimensional ratio of width W to length L is within the preferred ranges as given by the curves of Fig. 2, the lower frequency longitudinal mode Fyy is considerably stronger than that of the higher frequency mode Fys. Where the secondary resonant frequency Fys has a frequency value and a ratio of capacities relatively high with respect to those of the desired resonance Fyy, the importance of the former is decreased.

curve A of Fig. 2. a 0 angle of suba p angle of Asub- As another example from a crystal element I having stantially +8.5 degrees and stantially 34 degrees has a maximum positive temperature coeiiicient for its longitudinal mode vibrational frequency along the length dimension L of about +.4 part per million per degrees centigrade and a zero temperature coeicient at the dimensional ratios of about 0.36 and 0.51. Where crystals having the. lowest temperature coeiilcient over the widest temperature range are desired, those selected from the curve A of Fig. 2 may be used, the 6 angle thereof fbeing about +8.5 degrees, the p angle being between 32 and 36 degrees, and the dimensional ratio being a value within the ranges given by thecurve A of Fig. 2. .x

As an example from the curve C of Fig. 2, a crysta1 element I having a 6 angle of substantially +5 degrees and a c angle of about 40 degrees has a temperature coeiilcient for its longitudinal mode resonant frequency of less than 0.2 part per million per degree centigrade for dimensional ratios of width W to length L between about 0.35 and 0.57. Over this ratio, the secondary resonant frequency F11/z changes by a considerable amount and hence it can be placed in a favorable position where it can do no harm to the desired longitudinal mode frequency Fyy which has the low temperature coeicient.

As another example fromA the curve C of Fig. 2, a crystal element I having a 0 angle of substantially +5 degrees and a p angle of substantially 45 degrees has a temperature coefiicient for its longitudinal mode frequency of less than one part sional ratio of width W to length L from about I 0.40 to 0.55.

certain dimensional ratios of width W to lengthl L. These two prominent resonant frequencies vIn these longitudinally vibrated crystals and especially in those having the orientation angles and dimensional ratios as given by the curve A of Fig. 2, the ilrst derivative ai and also the second derivative la2 of the frequency with temperature may be zero-similar to the crystal designated GT in my application Serial No. 180,921 filed December 21, 1937, now United States Patent 2,204,762 dated June 18, 1940, and hence they may have a very small frequency variation throughout a wide temperature range. At the same time, they are relatively small in size for a given frequency and can be economically made for operation considerably below kilocycles per second at the fundamental mode longitudinal vibration frequency which is dependent mainly on the length dimension L lying along the Y' axis of the quartz. AlsoA the dimensional ratio of axes` W to L can be varied over a wide range without aiTecting the desired low temperature coefficient of frequency and hence the one prominent undesired secondary resonance therein may be changed or moved to any convenient position without affecting the temperature ooeiiicient of the desired frequency.

The crystal elements described herein may be mounted in any suitable manner such as, for example, by rigidly clamping the electroded crystal plate I between one ormore pairs of opposite conductive clamping projections which may contact the electroded crystal plate I at opposite points of very small area along the nodal line of the crystal element I. Figs. 4'and 5 illustrate a suitable holder of this type;

Figs. 4 and 5 are front and side elevation views of a crystal holder unit which consists of an the desired series resonance frequency by reducelectroded quartz crystal plate I mounted by clamping means in an Isolantite or other insulating mounting block III and assembled Ainside an evacuated metal bulb II which is equipped with -at least three external conductive pin terminals I2 arranged for mounting in a suitable socket (not shown). As shown in Figs. 4 to 6, the quartz crystal plate I is provided with four separate electrodes 20, 2l, 22 and 23 which are formed integral with the opposite major surfaces of the crystal element I by depositing thereon thin films of metal, such as thin films of silver or aluminum deposited by evaporation in vacuum, or by any other suitable process.

As shown in Figs. 4 and 5, the electroded crystal element I is clamped along its nodal line 24 between four conductive contact clamping pins 26 and 26 which may be composed of gold-plated brass, the clamping points thereof being individually in contact with the four electrodes 20, 2 I, 22 and 23 of the crystal element I. The two clampingv contact pins 26 which are disposed on one side of the crystal element I are fixed in the Isolantite mounting block III while the oppo- The mounted crystal plate I will be found to age over a period of as much as seven days after so adjusting it. Duringthis aging period, the resonance frequency rises and the eifective resistance decreases.l Suitable allowance for this aging may be made so that the crystal element I will meet the requirements after it has become stable.

Fig. 6 is a schematic diagram showing the electrical connections between the crystal electrodes 26, 2|, 22 and 23 and three of the pin terminals I2 which extend from the base or header assembly I3 of the bulb or tube I I`. As shown in Fig. 6, the electrode 20 is connected with one of the pin terminals I2, the crystal electrode 23 is connected with another of the pin terminals I2, and the crystal electrodes 2l and 22 are interconnected and connected with a third pin terminal I2 which is grounded. The two larger sitely disposed clamping contact pins 25 located on the opposite side of the `crystal element I are slidable in suitable brass bushings placed in openings in the mounting blockvIII. The clamping members 25 are pressed against the electroded crystal element I by means of two separate springs 2l which are secured to the outer surface of the mounting block I0. The pressure exerted by each of the springs 21 on the movable contacts 25 may be about 1 to 3 pounds or sui'llcient to hold the clamped crystal element I against bodily movement out of a predetermined position when placed between the two pairs of clamping points 25 and 26. v

The two pairs of clamping points 25 and 26 are oppositely disposed with respect to each other and axially disposed perpendicular to the major surfaces of the crystal element I and since they make contact only along the nodal line 24 of the crystal element I, there is a minimum of damping of the vibratory motion of the crystal element I. The nodal line 24 is inclined roughly 1l degrees with respect to the width dimension'W of the crystal element I as illustrated in Fig. 5. The crystal plate I is preferably clamped only along the nodal line 24 in order to obtain the minimum effective resistance at resonance. The mounting block I0 is resiliently supported within the metal bulb I I at or near its opposite ends by two phosphor bronze springs 30 and 3|. The

metal bulb II may be soldered vacuum tight to the header assembly I3. The vacuum within the tube I I may be made about 0.1 millimeter of mercury absolute. The crystal plate I is adjusted to crystal electrodes 2i and 22 may overlap as illustrated in Fig. 6 in order to reduce the capacity of the electroded crystal element I. The interconnection between the electrodes 2l and 22 may be made by extending the integral metal plating around the top or bottom edge of the crystal element I or by a flexible insulated wire within the tube II extending around the top of the mounting block Il and connected with the proper terminals of the clamping points 25 and 26. The

two pairs of clamping projections 25 and 26 serve not only to clamp the crystal element I to hold it in position but also to establish the individual electrical connections with its electrodes 20 to 23 of .the crystal element I.

Since the crystal electrodes 2i and 22 of Fig. 6 are interconnected, a continuous conductive clamping spring surrounding the crystal element I may be utilized for clamping the crystal element I between one or more pairs of clamping projections extending from the opposite sides thereof and also contacting the electrodes 2I and 22 for simultaneously providing the interconnection between the two larger crystal electrodes 2I' and 22 of Fig. 6. At points where such projections may contact the high potential electrodes 20 and 23, they may be linsulated therefrom by removing the plating 20 and 23 directly under the points of contact. Such a spring arrangement may be of the type shown in application Serial No. 248,437 filed December 30, 1938, by W. L. Bond, now United States Patent 2,203,486 dated June 4, 1940, but free of insulation between the spring'parts. The electrical connections for the two remaining crystal electrodes 20 and 23 may then be established by meansv of two separate wires soldered thereto preferably along the nodal line 24 of the crystal element I. l

Alternatively instead of being mounted by clamping as illustrated in Figs. 4 to 6, the electroded crystal plate I may be mounted and electrically connected by soldering, cementing or otherwise attaching four fine conductive supporting wires directly to the bare quartz or to a thickened part of the electroded crystal element l along its nodal line 24 or along its central width dimension line W. The fine supporting wiresreferred to may be conveniently soldered to four narrow stripes of baked silver paste or other metallic paste which has been previously applied along the central width dimension line which may consist of pure silver applied by the known evaporation in vacuum process. Such fine supporting wires secured to the electroded crystal element I may extend horizontally from the vertical major surfaces of the crystal element I and at their opposite ends be attached by solder, for example, to four vertical spring conductive wires carried by the press or other part of an evacuated glass tube II. The spring wires may have one or more bends therein to resiliently absorb mechanical vibrations. Also, bumpers or stops of soft resilient material may be spaced adjacent the edges or other parts of the crystal element I to limit the bodily displacement thereof when the device is subjected to mechanical shock. It will be understood that any holder which will give stability and a relatively high Q or reactance resistance ratio for the crystal element I may be utilized for mounting the crystal element I.

Although this invention has been described and illustrated in relation to specific arrangements, it is to be understood that it is capable of application in other organizations and is therefore not to be limited to the particular embodiments disclosed, but only by the scope of the appended claims and the state of the prior art.

What is claimed is:

1. A piezoelectric quartz crystal element adapted to vibrate at a frequency of low temperature coemcient dependent mainly upon the length or longest dimension of its major surfaces, said length dimension being substantially in the plane of a Y axis and the vZ axis and inclined or disposed at an angle within the range from substantially to +8.5 degrees with respect to said Y axis, said major surfaces being inclined at an angle Within the range from substantially 30 to 48 degrees with respect to said YZ plane, said length dimension being a value in accordance with the value of said frequency, the ratio of the Width dimension of said major surfaces with respect to said length dimension thereof being one of the values within the range from substantially 0.25 to 0.85.

2. A, piezoelectric quartz crystal element adapted to vibrate at a frequency of low temperature coeilcient dependent mainly upon the length or longest dimension of its major surfaces, said length dimension being substantially in the plane of a Y axis and the Z axis and inclined or disposed at an angle within the range from substantially +5 to +8.5 degrees with respect to said Y axis, said major surfaces being inclined at an angle within the range from substantially 30 to 48 degrees with respect to said YZ plane, the ratio of thev .width dimension of said major surfaces with respect to said length dimension thereof being one of the values within the range from substantially 0.25 to 0.85, said length dimension expressed in centimeters being a value within the range from substantially 250 to 280 divided by said frequency expressed in kilocycles per second.

3. A piezoelectric quartz crystal element adapted to vibrate at a frequency of low temperature coeilicient dependent mainly upon the length or longest dimension of its major surfaces, said length dimension being substantially in the plane of a Y axis and the Z axis and inclined ordisposed at an angle within the range from substantially 0 to +10.0 degrees with respect to said Y axis, said major surfaces being inclined at an angle within the range from substantially 30 to 48 degrees with respect to said YZ plane.

surfaces"`with respect to said the ratio of the width dimension of said major length dimension thereof being one of the values within the range from substantially 0.25 to 0.85, said angles and said dimensional ratio being values as given by the curves of Fig. 2.

4. A piezoelectric quartz crystalelement adapted to vibrate at a frequency of low temperature coeii'lcient dependent mainly upon the length or longest dimension'of its major surfaces, said length 'dimension being substantially in the plane of a Y axis and the Z axis and inclined or disposed at an angle within the range from substantially 0 to +l0.0 degrees with respect to said `Y axis, said maior surfaces being inclined at an angle within the range from substantially 30 to 48 degrees with respect to said YZ plane, the ratio of the width dimension of said major surfaceswith respect to said length dimension thereof being one of the values within the range from substantially 025 to 0.85, said length dimension expressed in centimeters being a value within the range from substantially 250 to 280 divided by said frequency expressed in kilocycles per second, said angles and said dimensional ratio being values as given by the curves of Fig. 2.

5. A piezoelectric quartz crystal element adapted to vibrate at a frequency of low temperature coeillcient dependent mainly upon the length or longest dimension of its major surfaces, said length dimension being substantially ln the plane of a Y axis and the Z axis and inclined substantially +8.5 degrees with respect to said Y axis, said major surfaces being inclined at an angle within the range from substantially 30 to 40 degrees with respect to said YZ plane, the' ratio of the width dimension of said major surfaces with respect to said length dimension thereof being one of the values within the'range from substantially 0.30 to 0.56.

6. A piezoelectric quartz crystal element adapted to vibrate at a frequency of low temperature .coeillcient dependent mainly upon the length or longest dimension of its major surfaces, said length dimension being substantially in the 'plane o`f a Y axis and the Z axis and inclined substantially +8.5 degrees with respect to said Y axis, said major surfaces being inclined at an angle within the range from substantially 30 to 40 degrees with respect to said YZ plane, the ratio of the width dimension of said major surfaces with respect to said length dimension thereof being one of the values within the range from substantially 0.30 to 0.56, said length dimension expressed in centimeters being substantially 280 divided by said frequency expressed in kilocycles per second.

7. A piezoelectric quartz crystal element adapted to vibrate at a frequency of low temperature coeillclent dependent mainly upon the length or longest dimensionof its major surfaces, said length dimension being of a Y axis and the Z axis and inclined substantially +8.5 degrees with respect to said Y axis, said major surfaces being inclined at an angle Within the range from substantially 30 to 40 degrees with respect to said YZ plane, the ratio of the width dimension of said major surfaces with respect to said length dimension thereof being one of the values within the range from substantially 0.30 to 0.56, said angle and said dimensional ratio being values as given by the curve A of Fig. 2.

8. A piezoelectric quartz crystal element adapted to vibrate at a frequency of low temperature substantially in the plane tially +8.5 degrees with respect to said Y axis,

said major surfaces being inclined at an angle within the range from substantially 30 to 40 degrees with respect to said YZ plane, the ratio of the width dimension of said major surfaces x with respect to said length dimension thereof being one of the values within the range from substantially 0.30 to 0.56, said length dimension expressed in centimeters being substantially 280 divided by said frequency expressed in kilocycles per second, said angle and said dimensional ratio being values as given by the curve A of Fig. 2.

9. A piezoelectric quartz crystal element adapted to vibrate at a frequency of low temperature coeflicient dependent mainly upon the length or longest dimension of its major surfaces, said length dimension being substantially in the 'plane of a Y axis and the Z axis and inclined substantially +8.5 degrees with respect to said Y axis, said major surfaces being inclined at an angle within the range from substantially 34 to 36 de- 25 grees with respect to said YZ plane, the ratio of the width dimension of said major surfaces with respect to said length dimension thereof being one of the values within the range from substantially 0.33 to 0.52, said length dimension expressed 3o in centimeters being substantially'\280 divided by said frequency expressed in kilocycles per second.

10. A piezoelectric quartz crystal element adapted to vibrate at a frequency of low temperature coefficient dependent mainly upon the length 35 or longest dimension of its major surfaces, said length dimension being substantially in the plane of a Y axis and the Z axis and inclined substantially +l.5 degrees with respect'to said Y axis,

said major surfaces being inclined at an angle 40 within the'range from substantially 35 to 40 degrees with respect to said YZ plane, the ratio of the width dimension of said major surfaces with..l respect to said length dimension thereof being one of the values within thejrange from substantially 0.30 to 0.56. i

11. A piezoelectric quartz crystal element adapted to vibrate at a frequency of low temperature coefficient dependent mainlyA upon the length or longest dimension of its major surfaces,

said length dimension being substantially in the plane of a Y axis and the Z axis and inclined substantially degrees with respect to said Y axis, said major surfaces being inclined at an angle within the range from substantially 35 to 55 40 degrees with respect to said YZ plane, the ratio of the width dimension of said maior surfaces with respect' to said length dimension thereof being one of the values within the range from substantially 0.30 to 0.56, said angle and said diso mensional ratio being values as given by the curve B of F18. 2.

i2. A piezoelectric quartz crystal element adapted to vibrate at a frequency of `low temperature coemcient dependent mainly upon the 6,5

length or longest dimension of its major surfaces, said length dimension .being substantially in the plane of a Y axis andthe Z axis and inclined substantially +5 degrees with respect to said Y axis, said major surfaces being inclined at an angle within the range from substantially 39 to 45 degrees with respect to said YZ plane, the ratio of the width dimension of said major surfaces with respect to said length dimension thereof being one of the values within the range from substantially 0.30 to 0.60.

13. A piezoelectric quartz crystal element adapted to vibrate at a frequency of low temperature coefficient dependent mainly upon the length or longest dimension of its maior surfaces, said length dimension being substantially in the plane of a Y axis and the Z axis and inclined substantially +5 degrees with respect to said Y axis, said major surfaces being inclined at an angle within the range from substantially 39 to 45 degrees with respect ,to said YZ plane, the ratio of the width dimension of said major surfaces with respect to said length dimension thereof being one ofthe values within the range from substantially 0.30 to 0.60, said angle and said dimensional ratio being values as given by the curve C of Fig. 2.

14. A piezoelectric quartz crystal element l adapted to vibrate at a frequency of low temperature coefiicient dependent mainly upon the length or longest dimension of its major surfaces, said length dimension being substantially in the plane` of a Y axis and the Z axis and disposed substantially zero degrees with respect to said Y axis,

said major surfaces being inclined at an angle within the range from substantially 45 to 50 de` grees with respect to said YZ plane, the ratio of the width dimension of said major surfaces with `respect to said length dimension thereof being one of the values within the range from substantially 0.25 to 0.85.

15. A piezoelectric quartz crystal element adapted to vibrate at a frequency of low temperature coefilclent dependent mainly up'on the length or longest dimension of its major surfaces, said length dirxien'sion being substantially in the plane of a Y axis and the Z axis and disposed substantially zero degrees with respect to said Y axis, said major surfaces being inclined at an angle within the range from substantially 45 to 50 degrees with respect to said YZ plane, the ratiq of the width dimension of said maior surfaces with respect to said length dimension thereof being one of the values withinthe range from substantially 0.25 to 0.85, said angle and said dimensional ratio being values as given by the curve D of Fig. 2.

16. A quartz piezoelectric crystal element of low temperature coefilcient adapted to`vibrate at a frequency dependent mainly upon the length or longest dimension of) its major surfaces, said length dimension being a value in accordance with the value of said frequency, said` maior surfaces being substantially parallel to the 

